There has been a wide range of solutions proposed to solve these cosmological tensions which requires new physics/modifications in the early Universe i.e. pre-recombination era as well as in the late Universe. Not a single model yet fully solves both \(H_0\)  and \(S_8\)  tensions simultaneously.
The class of solutions which invokes modifications of the late-time Universe dynamics in dark energy generally leaves \(r_s\)  unaffected by construction and has been studied extensively in recent times.
The higher value of \(H_0\)  is then accommodated by a smaller value of \(\Omega _{\rm DE}\)  or \(\Omega _m\)  at redshift below \(z_*\)  such that \(d_A(z_*)\)  stays unaffected as well. This can be done for instance by invoking variations in the dark-energy equation of state [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]} or decaying dark matter [11]} [12]} or non-thermal dark matter [13]} with certain level of success.
